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Strength of Materials: Torsion

Length: 06 Minutes 42 Seconds

## Torsion

Torsion is caused by a twisting force called torque. To calculate torque, equation 1 would be used. Torque that is positive goes in the counter-clockwise direction; negative torque goes in the clockwise direction. If you're confused use your right hand and point your thumb towards yourself, the way your fingers curl represents a positive torque.

(1)

## Torsional Stress

All stress caused by torsion is shear stress. For a circular rod, maximum stress is found on the surface, and it decreases linearly to zero as you approach the central axis, refer to the figure below. For objects that are not circular the resulting stress field is different. This will be discussed in another section.

To calculate the stress due to torsion equation 2 would be used.

(2)

To calculate the polar moment of inertia for a circular rod equation 3 would be used.

(3)

## Angle of Twist

To calculate the angle of twist equation 4 would be used; answer will be in radians. This equation only considers constant cross-sectional area.

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## Torsional Striffness

Sometimes it might be necessary to calculate the torsional stiffness of a part. The reason for this could be to conduct a vibrational analysis, or to get a general idea of how strong that part is when the loading is not known. To calculate torsional stiffness equation 5 would be used.

(5)

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